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Simplifying 3y2 + -162y + 585 = 0 Reorder the terms: 585 + -162y + 3y2 = 0 Solving 585 + -162y + 3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(195 + -54y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(195 + -54y + y2)' equal to zero and attempt to solve: Simplifying 195 + -54y + y2 = 0 Solving 195 + -54y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-195' to each side of the equation. 195 + -54y + -195 + y2 = 0 + -195 Reorder the terms: 195 + -195 + -54y + y2 = 0 + -195 Combine like terms: 195 + -195 = 0 0 + -54y + y2 = 0 + -195 -54y + y2 = 0 + -195 Combine like terms: 0 + -195 = -195 -54y + y2 = -195 The y term is -54y. Take half its coefficient (-27). Square it (729) and add it to both sides. Add '729' to each side of the equation. -54y + 729 + y2 = -195 + 729 Reorder the terms: 729 + -54y + y2 = -195 + 729 Combine like terms: -195 + 729 = 534 729 + -54y + y2 = 534 Factor a perfect square on the left side: (y + -27)(y + -27) = 534 Calculate the square root of the right side: 23.108440017 Break this problem into two subproblems by setting (y + -27) equal to 23.108440017 and -23.108440017.Subproblem 1
y + -27 = 23.108440017 Simplifying y + -27 = 23.108440017 Reorder the terms: -27 + y = 23.108440017 Solving -27 + y = 23.108440017 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + y = 23.108440017 + 27 Combine like terms: -27 + 27 = 0 0 + y = 23.108440017 + 27 y = 23.108440017 + 27 Combine like terms: 23.108440017 + 27 = 50.108440017 y = 50.108440017 Simplifying y = 50.108440017Subproblem 2
y + -27 = -23.108440017 Simplifying y + -27 = -23.108440017 Reorder the terms: -27 + y = -23.108440017 Solving -27 + y = -23.108440017 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + y = -23.108440017 + 27 Combine like terms: -27 + 27 = 0 0 + y = -23.108440017 + 27 y = -23.108440017 + 27 Combine like terms: -23.108440017 + 27 = 3.891559983 y = 3.891559983 Simplifying y = 3.891559983Solution
The solution to the problem is based on the solutions from the subproblems. y = {50.108440017, 3.891559983}Solution
y = {50.108440017, 3.891559983}
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